My son also had horrible excema, but just on the palm of his left hand. For YEARS, I bought every single over the counter "eczema" lotion that ever existed. I took him to the dermatologist, and all they ever did was prescribe a steroid cream (which is not good to use frequently). I started him on a GF diet, and that helped. Then I put him on a dairy free diet as well, which helped his eczema even more - however, he said being dairy free was too hard, so I let it go, but he still eats GF (which I highly recommend for your daughter).
Recently, I took my son to an herbalist/Chinese medicine doctor, and she gave me herbal pills to give him for 2 weeks. The 2 weeks is almost up, and his eczema is almost all cleared up! These herbal pills are amazing!! They are tiny and round, and he has to take 20 a day - 10 in the morning and 10 at night. Since your daughter is 3 and can't swallow pills (I'm assuming), I'm sure it would be fine to crush them up in a pill crusher and put it in juice (but ask the herbalist, of course)! I can't say enough great things about Chinese medicine/herbs. It has helped the most!
I know you said you live in a small town, but even if you would have an hour drive (or more) to an herbalist, it will be worth it - I promise! Good luck.